The DFT of a sequence x (n) of length N may be expressed in matrix form as follows
X=Wx
where x = [x(0), x(1), ... , x(N - 1)]T is a vector containing the signal values and X is a vector containing the DFT coefficients X (k),
(a) Find the matrix W.
(b) What properties does the matrix W have?
(c) What is the inverse of W?